Is there 2 numbers that multiply to -84 and add up to 25?

Answer 1

Let the number be 'm' & 'n'

mn = -84

m + n = 25

Algebraically rearrgange

m = -84/n

m = 25 - n

Substitute for 'm'

-84/n = 25 - n

Multiply through by 'n'

-84 = 25n - n^2

n^2 - 25n - 84 = 0

It is now in Quadratic Form . You can either try and factor or apply the Quadratic Eq'n.

n = { - - 25 +/- sqrt[(-25)^2 - 4(1)(-84)]} / 2(1)

n = { 25 +/- sqrt[ 625 + 336]} / 2

n = { 25 +/- sqrt[961]} / 2

n = {25 +/- 31}/2

n = 56/2 or -6/2

n = 28 or -3

Hence m = -3 or 28

Answer 2

-3 and 28

x*y=-84 x+y=25 (What's known)

x=-84/y x=25-y (Solve for x)

-84/y=25-y (Set them equal using the solved x's)

-84=25y-y^2 (Simplify)

y^2-25y-84=0 (Solve for 0)

(y-28)(y+3)=0 (Factor)

y=28|y=-3 (Solve for solutions)

Factors of 84:

1|84

2|42

3|28

4|21

6|14